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Chapter 7 Graphing Linear Equations Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7-1 Chapter Sections 7.1 – The Cartesian Coordinate System and Linear Equations in Two Variables 7.2 – Graphing Linear Equations 7.3 – Slope of a Line 7.4 – Slope-Intercept and Point-Slope Forms of a Linear Equation 7.5 – Graphing Linear Inequalities 7.6 – Functions Copyright © 2015, 2011, 2007 Pearson Education, Inc. Copyright © 2011 Pearson Education Chapter 7-2 2 Graphing Linear Inequalities Copyright © 2015, 2011, 2007 Pearson Education, Inc. Copyright © 2011 Pearson Education Chapter 7-3 3 Linear Inequalities A linear inequality in two variables can be written in one of the following forms: ax + by < c, ax + by > c, ax + by c, ax + by c where a, b, and c are real numbers and a and b are not 0 Examples: 2x + 3y > 25 – x – 2y 3 3y < 4x - 9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Copyright © 2011 Pearson Education Chapter 7-4 4 Graph Linear Inequalities 1. Replace the inequality symbol with an equals sign. 2. Draw the graph of the equation in step 1. If the original inequality contained the a or , draw the boundary line using a solid line. If the original inequality contained the symbol < or >, draw the boundary line using a dashed line. 3. Select any point not on the boundary line and determine if this point is a solution to the original inequality. If it is, shade the region on the side of the line containing this point. If it is not a solution, shade the region on the side of the line not containing the point. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Copyright © 2011 Pearson Education Chapter 7-5 5 Graph Linear Inequalities Graph y < 2x + 1. dashed line Checkpoint (0, 0 ) satisfies the inequality. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Copyright © 2011 Pearson Education Chapter 7-6 6